Question

A body is projected vertically up from the surface of the earth with a velocity half of the escape velocity. The ratio of the maximum height of ascent of the body and radius of the earth is

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:4$

Answer 1

Answer: (D)

$1:4$

Given $V=\frac{1}{2}{V}_e$
But $V_e=\sqrt{\frac{2GM}{R}}$
$\Rightarrow V=\sqrt{\frac{GM}{2R}}$
$\Rightarrow h=\frac{V^2}{2g}$
$\Rightarrow g=\frac{GM}{R^2}$
$\Rightarrow h=\frac{\frac{GM}{2R}}{2\frac{GM}{R^2}}$
$\Rightarrow h=\frac{R}{4}$